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Bresenham's line drawing algorithm
The Bresenham's line drawing algorithm is an incremental scan conversion algorithm that uses only integer calculations. It works by calculating the difference between the ideal y value and the actual plotted pixel y value at each x value, and determining whether to plot the pixel above or below the line based on whether this difference is positive or negative. The algorithm takes the line endpoints as input, calculates the change in x and y per step, sets an initial decision parameter, and then iteratively plots pixels, updating the decision parameter to determine whether to plot above or below the line at each step.
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Introduction to Bresenham's Algorithm, an incremental scan conversion algorithm utilizing only integer calculations.
Detailed mathematical expressions relevant to Bresenham's line drawing, including calculations for dlower, dupper, and associated equations.
Step-by-step instructions on implementing Bresenham's algorithm to plot a line from given endpoints with example calculations for specific points.
Closure of the presentation with a thank you note.
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Bresenham's line drawing algorithm
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- 2. INTRODUCTION- • THE BRESENHAMALGORITHM IS A INCREMENTAL SCAN CONVERSION ALGORITHM. • THE BIG ADVANTAGE OF THIS ALGORITHM IS THAT, IT USES ONLY INTEGER CALCULATIONS.
- 3. • dlower. =y−yk =m(Xk+1)+b−Yk •dupper. =(yk+1)−y =Yk+1−m(Xk+1)−b • dlower−dupper=2m(xk+1)−2yk+2b−1 • dx(dlower − dupper) =dx(2dydx(xk+1)−2yk+2b−1. =2dy.xk−2dx.yk+C • Pk=2dy.xk−2dx.yk+C • Pk+1=pk+2dy−2dx(yk+1−yk) • P0=2dy−dx
- 4. ALGORITHM- 1) INPUT END-POINTSOF THE LINE (X1 ,Y1 ,X2 ,Y2) 2) X = X1 AND Y = Y1 3) CALCULATE DX AND DY 4) PO = (2*DY) - DX 5) IF PK <0 PLOT(XK+1 , YK) SET PK+1= PK + (2DY) ELSE PLOT(XK+1 ,YK+1) SET PK+1= P+(2DY)-(2DX) 1) REPEAT STEP 5 (DX) TIMES. 2) END
- 5. Draw a linefrom (20,10) to (30,18)- dx = (30-20) = 10 dy = (18-10) = 8 Po = (2*dy) - dx =16-10 = 6 k Pk Plotted pixel (x,y) 0 6 (21,11) 1 2 (22,12) 2 -2 (23,12) 3 4 (24,13) 4 10 (25,14) 5 6 (26,15) 6 2 (27,16) 7 -2 (28,16) 8 14 (29,17) 9 10 (30,18)
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